On the applicability of Marshallian partial-equilibrium analysis

Marshallian partial-equilibrium analysis is fully justified for well-behaved (downward sloping and consistent with consumer surplus) Marshallian demand functions. However, a demand function is well-behaved only if it is the demand for a neutral good with no income effects. In a two-good setting with a normal good and a numéraire, this paper proposes a weaker concept of well-behavedness, which requires a demand function to be well-behaved only for large income levels. It also provides necessary and sufficient conditions for a utility function to generate a demand function for a normal good which is well-behaved in this sense. This result clarifies the scope and limitations of the partial-equilibrium analysis in terms of agents' characteristics within the two-good setting.